Sky Sports reports how the 25-year-old is under contract at the Britannia Stadium until 2014, but with a number of rival Premier League clubs monitoring his situation, the Potters hope to tie the central defender to a new long-term deal.
Shawcross has been a virtual ever-present for Stoke over the past few seasons, since joining Tony Pulis' side in 2008, following his £1million release from Manchester United.
Red Devils boss Sir Alex Ferguson felt at the time that the youngster had no future at Old Trafford, and so allowed him to leave after graduating from the academy, as he began his search for regular first-team football.
In the four years since, the centre-back has established himself as one of the brightest young defenders in the division, prompting admiring glances - not only from former club United - from Chelsea and Spurs as well.
Andre Villas-Boas has already strengthened his defensive ranks with the addition of Jan Vertonghen during his short stint at White Hart Lane. However, with the former Ajax star being deployed more often at left-back, the Portuguese boss could venture back into the market in January.
Meanwhile, Blues boss Roberto Di Matteo has also been credited with an interest in signing Shawcross, in a bid to add more steel to a Stamford Bridge rearguard that is currently without the services of suspended skipper John Terry, who continues to serve his four-match Football Association ban.
However, any hopes that the Premier League trio might have had of securing the fringe England international's future have been dashed, after Stoke chairman Peter Coates reiterated his desire to keep him at the club.
"Ryan is an important player for us," he told The Sentinel. "And we want to keep him and make him secure. You try to look after your assets.
"He has developed his career at this football club and we want him to stay, so it's up to us to find a way of keeping him."